DistributionCategory(R)

distro.spad line 595 [edit on github]

Category of distributions formally given by moments.

0 : () -> %

0 is the Dirac distribution

= : (%, %) -> Boolean
from BasicType
^ : (%, PositiveInteger) -> %

x^k constructs the distribution of the kth power of the random variable with distribution X by picking every k-th moment.

booleanConvolution : (%, %) -> %

booleanConvolution(x, y) returns the boolean convolution of the distributions x and y

booleanCumulant : (%, PositiveInteger) -> R

booleanCumulant(x, n) returns the n-th boolean cumulant of the distribution x

booleanCumulants : % -> Sequence(R)

booleanCumulants(x) returns the sequence of boolean cumulants of the distribution x.

classicalConvolution : (%, %) -> %

classicalConvolution(x, y) returns the classical convolution of the distributions x and y

classicalCumulant : (%, PositiveInteger) -> R

classicalCumulant(x, n) returns the n-th classical cumulant of the distribution x

classicalCumulants : % -> Sequence(R)

classicalCumulants(x) returns sequence of classical cumulants of the distribution x

coerce : % -> OutputForm
from CoercibleTo(OutputForm)
freeConvolution : (%, %) -> %

freeConvolution(x, y) returns the free convolution of the distributions x and y

freeCumulant : (%, PositiveInteger) -> R

freeCumulant(x, n) returns the n-th free cumulant of the distribution x

freeCumulants : % -> Sequence(R)

freeCumulants(x) returns the sequence of free cumulants of the distribution x.

hankelDeterminants : % -> Stream(R)

hankelDeterminants(x) returns the stream of hankel determinants of the distribution x.

jacobiParameters : % -> Record(an : Stream(R), bn : Stream(R)) if R has Field

jacobiParameters(x) returns the pair of streams of Jacobi parameters of the distribution x.

jacobiParameters : % -> Record(an : Stream(Fraction(R)), bn : Stream(Fraction(R))) if R has IntegralDomain and R hasn't Field

jacobiParameters(x) returns the pair of streams of Jacobi parameters of the distribution x.

latex : % -> String
from SetCategory
moment : (%, NonNegativeInteger) -> R

moment(x, n) returns the n-th moment of the distribution x

moments : % -> Sequence(R)

moments(x) returns the sequence of moments of the distribution x

monotoneConvolution : (%, %) -> %

monotoneConvolution(x, y) returns the monotone convolution of the distributions x and y

monotoneCumulants : % -> Sequence(R) if R has Algebra(Fraction(Integer))

monotoneCumulants(x) returns the sequence of monotone cumulants of the distribution x.

orthogonalConvolution : (%, %) -> %

orthogonalConvolution(x, y) returns the orthogonal convolution of the distributions x and y

orthogonalPolynomials : % -> Stream(SparseUnivariatePolynomial(R)) if R has Field

orthogonalPolynomials(x) returns the stream of orthogonal polynomials.

orthogonalPolynomials : % -> Stream(SparseUnivariatePolynomial(Fraction(R))) if R has IntegralDomain and R hasn't Field

orthogonalPolynomials(x) returns the stream of orthogonal polynomials.

subordinationConvolution : (%, %) -> %

subordinationConvolution(x, y) returns the subordination convolution of the distributions x and y

~= : (%, %) -> Boolean
from BasicType

CoercibleTo(OutputForm)

BasicType

SetCategory